Finite Group Databasebeta

← A4×#4005 #14512562

Subgroups — A4×#4005 #14512562

Order 1920.

372 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×A4×Dic10C211yesmaximal, characteristic
2A4×#704C212yesmaximal
3C22×#4005C311yesmaximal, characteristic, complemented, Hall
4C2×C4×C5×A4C411yescharacteristic
5C2×A4×Dic5C411yescharacteristic
6C2×A4×Dic5C2211yescharacteristic
7A4×Dic10—22no—
8A4×#170—22no—
9C3×#4005—41nomaximal
10A4×#101—51nomaximal, Hall
11C23×Dic10C2×C311yescharacteristic
12C22×#704C2×C312yes—
13C2×#4005—32no—
14C2×#4005—31no—
15C2×#4005—31no—
16C22×C5×A4C2×C411yescharacteristic
17C2×C3×Dic10—41no—
18C4×C5×A4—21no—
19C3×#704—42no—
20A4×Dic5—21no—
21A4×Dic5D412yes—
22C2×Q8×A4—51no—
23A4×M16—52no—
24C23×C4×C5C3×C411yescharacteristic
25C23×Dic5C3×C411yescharacteristic
26C23×Dic5C22×C311yescharacteristic
27C22×Dic10—22no—
28C22×Dic10—31no—
29C22×Dic10—31no—
30C22×Dic10—31no—
31C22×Dic10—31no—
32C22×Dic10—62no—
33C2×#704—32no—
34C2×#704—32no—
35C2×#704—62no—
36C22×#170—22no—
37#4005—32no—
38#4005—31no—
39#4005—32no—
40#4005A411yescharacteristic, direct product factor
41C22×#101—51noSylow
42C2×C5×A4—21no—
43C2×C5×A4C22⋊C411yescharacteristic
44C2×C3×C4×C5—41no—
45C2×C3×Dic5—41no—
46C2×C3×Dic5—41no—
47C3×Dic10—82no—
48C3×#170—82no—
49Q8×A4—102no—
50C2×C4×A4—51no—
51C2×C4×A4—51no—
52C2×C4×A4AGL(1,𝔽5)11yescharacteristic
53C8×A4—102no—
54C3×#101—201no—
55C24×C5C2×C3×C411yescharacteristic
56C22×C4×C5—21no—
57C22×C4×C5—31no—
58C22×C4×C5—31no—
59C22×C4×C5—61no—
60C22×Dic5—21no—
61C22×Dic5—31no—
62C22×Dic5—32no—
63C22×Dic5—31no—
64C22×Dic5—31no—
65C22×Dic5—31no—
66C22×Dic5—61no—
67C22×Dic5C3×D412yes—
68C2×Dic10—32no—
69C2×Dic10—31no—
70C2×Dic10—31no—
71C2×Dic10—31no—
72C2×Dic10—62no—
73C2×Dic10—62no—
74C2×Dic10—62no—
75C2×Dic10—62no—
76C2×Dic10—62no—
77C2×Dic10—62no—
78C2×Dic10—62no—
79C2×Dic10—62no—
80C2×Dic10C2×A411yescharacteristic
81#704—32no—
82#704—62no—
83#704—62no—
84#704C2×A412yes—
85C2×#170—62no—
86C2×#170—62no—
87C23×Q8—51no—
88C22×M16—52no—
89C2×#101—151no—
90C2×#101—152no—
91C2×#101—151no—
92C22×C3×C5—41no—
93C5×A4#10111yescharacteristic, complemented
94C3×C4×C5—81no—
95C3×Dic5—42no—
96C3×Dic5—81no—
97C22×A4C2×AGL(1,𝔽5)11yescharacteristic
98C2×C3×Q8—201no—
99C4×A4—21no—
100C4×A4—52no—
101C4×A4—101no—
102C3×M16—202no—
103C23×C5—21no—
104C23×C5—31no—
105C23×C5—31no—
106C23×C5—61no—
107C23×C5C3×C22⋊C411yescharacteristic
108C2×C4×C5—31no—
109C2×C4×C5—61no—
110C2×C4×C5—61no—
111C2×C4×C5—61no—
112C2×C4×C5—61no—
113C2×C4×C5C4×A411yescharacteristic
114C2×Dic5—32no—
115C2×Dic5—31no—
116C2×Dic5—32no—
117C2×Dic5—32no—
118C2×Dic5—32no—
119C2×Dic5—31no—
120C2×Dic5—61no—
121C2×Dic5—61no—
122C2×Dic5—61no—
123C2×Dic5—61no—
124C2×Dic5C4×A411yescharacteristic
125C2×Dic5C22×A411yescharacteristic
126Dic10—22no—
127Dic10—62no—
128Dic10—62no—
129Dic10—64no—
130Dic10—62no—
131#170—22no—
132#170—62no—
133C22×Q8—102no—
134C22×Q8—151no—
135C22×Q8—151no—
136C22×Q8—151no—
137C22×Q8—151no—
138C22×Q8—302no—
139C23×C4—51no—
140C23×C4—51no—
141C23×C4C3×AGL(1,𝔽5)11yescharacteristic
142C2×M16—152no—
143C2×M16—152no—
144C2×M16—302no—
145C22×C8—102no—
146#101—51no—
147#101—152no—
148#101—151no—
149#101—152no—
150C2×C3×C5—41no—
151C2×C3×C5—81no—
152C2×A4—21no—
153C2×A4C22⋊AGL(1,𝔽5)11yescharacteristic
154C3×Q8—402no—
155C2×C3×C4—41no—
156C2×C3×C4—201no—
157C2×C3×C4—201no—
158C3×C8—402no—
159C22×C5—31no—
160C22×C5—31no—
161C22×C5—31no—
162C22×C5—61no—
163C22×C5—61no—
164C22×C5—61no—
165C22×C5—61no—
166C22×C5C3×#10111yescharacteristic, complemented
167C22×C5C2×C4×A411yescharacteristic
168C4×C5—21no—
169C4×C5—61no—
170Dic5—21no—
171Dic5—32no—
172Dic5—61no—
173Dic5D4×A412yes—
174C24C2×C3×AGL(1,𝔽5)11yescharacteristic
175C2×Q8—51no—
176C2×Q8—151no—
177C2×Q8—151no—
178C2×Q8—152no—
179C2×Q8—151no—
180C2×Q8—302no—
181C2×Q8—302no—
182C2×Q8—302no—
183C2×Q8—302no—
184C2×Q8—302no—
185C2×Q8—302no—
186C2×Q8—302no—
187C2×Q8—302no—
188C22×C4—21no—
189C22×C4—31no—
190C22×C4—31no—
191C22×C4—52no—
192C22×C4—61no—
193C22×C4—101no—
194C22×C4—151no—
195C22×C4—151no—
196C22×C4—152no—
197C22×C4—151no—
198C22×C4—151no—
199C22×C4—301no—
200M16—52no—
201M16—152no—
202M16—302no—
203M16—302no—
204C2×C8—302no—
205C2×C8—302no—
206C3×C5—41noHall
207C22×C3—41no—
208A4#400511yescharacteristic, direct product factor
209C3×C4—81no—
210C3×C4—202no—
211C3×C4—401no—
212C2×C5—21no—
213C2×C5—31no—
214C2×C5—31no—
215C2×C5—61no—
216C2×C5A4×C22⋊C411yescharacteristic
217C23—21no—
218C23—31no—
219C23—31no—
220C23—61no—
221C23C3×C22⋊AGL(1,𝔽5)11yescharacteristic
222Q8—102no—
223Q8—302no—
224Q8—302no—
225Q8—302no—
226Q8—304no—
227C2×C4—31no—
228C2×C4—51no—
229C2×C4—51no—
230C2×C4—61no—
231C2×C4—61no—
232C2×C4—61no—
233C2×C4—61no—
234C2×C4—152no—
235C2×C4—152no—
236C2×C4—152no—
237C2×C4—151no—
238C2×C4—152no—
239C2×C4—151no—
240C2×C4—301no—
241C2×C4—301no—
242C2×C4—301no—
243C2×C4—301no—
244C2×C4A4×AGL(1,𝔽5)11yescharacteristic
245C8—102no—
246C8—302no—
247C2×C3—41no—
248C2×C3—81no—
249C5A4×#10111yescharacteristic, complemented, Sylow
250C22—31no—
251C22—31no—
252C22—31no—
253C22—61no—
254C22—61no—
255C22—61no—
256C22—61no—
257C22C3×#400511yescharacteristic, complemented
258C22C2×A4×AGL(1,𝔽5)11yescharacteristic
259C4—21no—
260C4—52no—
261C4—61no—
262C4—101no—
263C4—152no—
264C4—301no—
265C3—41noSylow
266C2—21no—
267C2—31no—
268C2—31no—
269C2—61no—
270C2A4×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2A4×C22⋊AGL(1,𝔽5)
commutatorC24×C5C2×C3×C4
FrattiniC22C2×A4×AGL(1,𝔽5)
FittingC23×C4×C5C3×C4
socleC23×C5C3×C22⋊C4
prime radicalC22×C5×A4C2×C4
cosocleC23×Dic5C22×C3
hypercenterC2×C4A4×AGL(1,𝔽5)
hypocenterC22×C5C3×#101
LCSG ▷ C24×C5 ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C22×#4005C3semidirect
40. #4005A4direct (N × H)
93. C5×A4#101semidirect
166. C22×C5C3×#101semidirect
208. A4#4005direct (N × H)
249. C5A4×#101semidirect
257. C22C3×#4005semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×A4×Dic102
A4×#7042
C22×#40053
C3×#40054
A4×#1015